Abstract
Recently, the theory and applications of soft set has brought the attention by many scholars in various areas. Especially, the researches of the theory for combining the soft set with the other mathematical theory have been developed by many authors. In this paper, we propose a new concept of soft fuzzy rough set by combining the fuzzy soft set with the traditional fuzzy rough set. The soft fuzzy rough lower and upper approximation operators of any fuzzy subset in the parameter set were defined by the concept of the pseudo fuzzy binary relation (or pseudo fuzzy soft set) established in this paper. Meanwhile, several deformations of the soft fuzzy rough lower and upper approximations are also presented. Furthermore, we also discuss some basic properties of the approximation operators in detail. Subsequently, we give an approach to decision making problem based on soft fuzzy rough set model by analyzing the limitations and advantages in the existing literatures. The decision steps and the algorithm of the decision method were also given. The proposed approach can obtain a object decision result with the data information owned by the decision problem only. Finally, the validity of the decision methods is tested by an applied example.
Similar content being viewed by others
References
Aktas H, Cagman N (2007) Soft sets and soft groups. Inform Sci 177: 2726–2735
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20: 87–96
Bi YX, McClean S, Anderson T (2006) Combining rough decisions for intelligent text mining using Dempsters rule. Artif Intell Rev 26: 191–209
Bonikowski Z, Bryniariski E, Skardowska VW (1998) Extension and intensions in the rough set theory. Inform Sci 107: 149–167
Chen D, Tsang EC, Yeung DS, Wang X (2005) The parametrization reduction of soft sets and its applications. Comput Math Appl 49: 757–763
Chen D, Wang C, Hu Q (2007) A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Inform Sci 177: 3500–3518
Davvaz B, Dudek W, Jun Y (2006) Intuitionistic fuzzy Hv-submodules. Inform Sci 176: 285–300
Deng JL (1986) Theory of grey system. Huazhong University of Science and Technology Press, Wuhan
Faustino CP, Pinheiro CAM, Carpinteiro OA, Lima I (2011) Time series forecasting through rule-based models obtained via rough sets. Artif Intell Rev 36: 199–310
Feng F, Jun YB, Zhao XZ (2008) Soft semirings. Comput Math Appl 56: 2621–2628
Feng F, Li YM, Violeta LF (2010a) Application of level soft sets in decision making based on interval-valued fuzzy soft sets. Comput Math Appl 60: 1756–1767
Feng F, Jun YB, Liu XY, Li LF (2010b) An adjustable approach to fuzzy soft set based decision making. J Comput Appl Math 234: 10–20
Feng F, Liu XY, Violeta LF, Jun YB (2011) Soft sets and soft rough sets. Inform Sci 181: 1125–1137
Gau WL, Buehrer DJ (1993) Vague sets. IEEE Trans Syst Man Cybernet 23(2): 610–614
Gong ZT, Sun BZ, Chen DG (2008) Rough set theory for the interval-valued fuzzy information systems. Inform Sci 178: 1968–1985
Gorzalzany MB (1987) A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 21: 1–17
Greco S, Matarazzo B, Slowinski R (2002) Rough approximation by dominance relations. Int J Intell Syst 17: 153–171
Huang ZX, Lu XD, Duan HL (2011) Context-aware recommendation using rough set model and collaborative filtering. Artif Intell Rev 35: 85–99
Jiang YC, Tang Y, Chen QM, Liu H, Tang JC (2010) Interval-valued intuitionistic fuzzy soft sets and their properties. Comput Math Appl 60: 906–918
Jun YB (2008) Soft BCK/BCI-algebras. Comput Math Appl 56: 1408–1413
Jun YB, Park CH (2008) Applications of soft sets in ideal theory of BCK/BCI-algebras. Inform Sci 178: 2466–2475
Kong Z, Gao LQ, Wang LF, Steven L (2008) The normal parameter reduction of soft sets and its algorithm. Comput Math Appl 56: 3029–3037
Kong Z, Gao LQ, Wang LF (2009) Comment on a fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 223: 540–542
Li TJ, Leung Y, Zhang WX (2008) Generalized fuzzy rough approximation operators based on fuzzy coverings. Int J Approx Reason 48: 836–856
Liu G, Sai Y (2009) A comparison of two types of rough sets induced by coverings. Int J Approx Reason 50: 521–528
Liu G, Zhu W (2008) The algebraic structures of generalized rough set theory. Inform Sci 178: 4105–4113
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3): 589–602
Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44: 1077–1083
Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45: 555–562
Majumdara P, Samantab SK (2010) Generalized fuzzy soft sets. Comput Math Appl 59: 1425–1432
Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 37: 19–31
Molodtsov D (2004) The theory of soft sets (in Russian). URSS Publishers, Moscow
Muhammad IA (2011) A note on soft sets, rough soft sets and fuzzy soft sets. Appl Soft Comput 11: 3329–3332
Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11: 341–356
Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer, Dordrecht
Pawlak Z, Skowron A (2007) Rudiments of rough sets. Inform Sci 177: 3–27
Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203: 412–418
Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fundam Inform 27: 245–253
Sun BZ, Gong ZT, Chen DG (2008) Fuzzy rough set for the interval-valued fuzzy information systems. Inform Sci 178: 2794–2815
Wu WZ, Zhang WX (2004) Constructive and axiomatic approaches of fuzzy approximation operators. Inform Sci 159: 233–254
Wu WZ, Mi JS, Zhang WX (2003) Generalized fuzzy rough sets. Inform Sci 151: 263–282
Xu W, Ma J, Wang SY, Hao G (2010) Vague soft sets and their properties. Comput Math Appl 59: 787–794
Yan JA (1998) Theory of measures. Science Press, Beijing
Yang XB, Lin TY, Yang JY, Li Y, Yu DJ (2009) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58: 521–527
Yao YY (1998a) Constructive and algebraic methods of the theory of rough sets. Inform Sci 109: 21–47
Yao YY (1998b) Relational interpretations of neighborhood operators and rough set approximation operators. Inform Sci 111: 239–259
Yao YY (1998c) Generalized rough set model. In: Polkowski L, Skowron A (eds) Rough sets in knowledge discovery 1. Methodology and applications. Physica-Verlag, Heidelberg, pp 286–318
Yao YY, Lin TY (1996) Generalization of rough sets using modal logic. Intell Autom Soft Comput Int J 2: 103–120
Zadeh LA (1965) Fuzzy sets. Inform Control 8: 338–353
Zhu W (2009) Relationship between generalized rough sets based on binary relation and covering. Inform Sci 179: 210–225
Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46: 39–59
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sun, B., Ma, W. Soft fuzzy rough sets and its application in decision making. Artif Intell Rev 41, 67–80 (2014). https://doi.org/10.1007/s10462-011-9298-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10462-011-9298-7